I'm not far off making commander and will get my new ship token, however I've grown quite fond of my current little science vessel. I wondered if it's possible to, instead of getting a new ship, upgrade my existing one to have things such as extra weapon slots fore and aft etc that I would get on the next level of ship?

There isn't a way to increase ship stats except via some captain skills. But your T2 ships is still quite viable in the PvE game. During the early testing of the F2P build on tribble, the economy was not entirely in place. As a result player could not afford to new ships as we levelel up as they required some dilithium grinding. And very little dilithium was being rewards were in the game. So what player did was to get their T2 ships and forgo their T3 ships to be able to afford to purchase their T4 ships. We kept upgrading the equipment and weapons of the T2 ships and kept using them.

That the rate that most player levels, getting their T4 ship was just about when we started to encounter the Romulans. Fighting a Romulan Battleship in a T2 ship is possible but very, very tough for even an experienced player. Some players took their T2s ships all the way to Read Admiral.

I always thought the best way to handle this would be having the option to "modify" your ship to have a scaling hull that gets better with level (like the various shuttles/fighters do now).

Ships would still maintain the same BOff/device/weapon/console slots and whathaveyou, thus giving INCENTIVE to use ships unlocked at higher tier, and making upgraded lower-tier ships a viable option, but not stupidly unbalanced.